Optimal. Leaf size=33 \[ \frac{44}{125 (5 x+3)}-\frac{121}{250 (5 x+3)^2}+\frac{4}{125} \log (5 x+3) \]
[Out]
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Rubi [A] time = 0.0298787, antiderivative size = 33, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ \frac{44}{125 (5 x+3)}-\frac{121}{250 (5 x+3)^2}+\frac{4}{125} \log (5 x+3) \]
Antiderivative was successfully verified.
[In] Int[(1 - 2*x)^2/(3 + 5*x)^3,x]
[Out]
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Rubi in Sympy [A] time = 5.34847, size = 26, normalized size = 0.79 \[ \frac{4 \log{\left (5 x + 3 \right )}}{125} + \frac{44}{125 \left (5 x + 3\right )} - \frac{121}{250 \left (5 x + 3\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**2/(3+5*x)**3,x)
[Out]
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Mathematica [A] time = 0.017457, size = 31, normalized size = 0.94 \[ \frac{440 x+8 (5 x+3)^2 \log (10 x+6)+143}{250 (5 x+3)^2} \]
Antiderivative was successfully verified.
[In] Integrate[(1 - 2*x)^2/(3 + 5*x)^3,x]
[Out]
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Maple [A] time = 0.008, size = 28, normalized size = 0.9 \[ -{\frac{121}{250\, \left ( 3+5\,x \right ) ^{2}}}+{\frac{44}{375+625\,x}}+{\frac{4\,\ln \left ( 3+5\,x \right ) }{125}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^2/(3+5*x)^3,x)
[Out]
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Maxima [A] time = 1.32894, size = 38, normalized size = 1.15 \[ \frac{11 \,{\left (40 \, x + 13\right )}}{250 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} + \frac{4}{125} \, \log \left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x - 1)^2/(5*x + 3)^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.212307, size = 50, normalized size = 1.52 \[ \frac{8 \,{\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) + 440 \, x + 143}{250 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x - 1)^2/(5*x + 3)^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.247232, size = 24, normalized size = 0.73 \[ \frac{440 x + 143}{6250 x^{2} + 7500 x + 2250} + \frac{4 \log{\left (5 x + 3 \right )}}{125} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)**2/(3+5*x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.205767, size = 32, normalized size = 0.97 \[ \frac{11 \,{\left (40 \, x + 13\right )}}{250 \,{\left (5 \, x + 3\right )}^{2}} + \frac{4}{125} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x - 1)^2/(5*x + 3)^3,x, algorithm="giac")
[Out]